We obtain a strong law of large numbers and a functional central limit theorem, as t → ∞, for the number of records up to time t and the Lebesgue measure (length) of the subset of the time interval [0, t] during which the Poisson process is in a record lifetime. strong law of large numbers.

In this paper, a new definition of locally convex L-topological vector spaces is given. The relationship between this new definition and the previous definition of locally convex L-topological vector spaces given by Yan and Fang in 1999 is investigated. Moreover, the concept of generalized L-fuzzy semi-norm is introduced. By using a family of generalized L-fuzzy semi-norms, a characterization o...

The concepts of L-convex function and M-convex function have recently been introduced by Murota as generalizations of submodular function and base polyhedron, respectively, and discrete separation theorems are established for L-convex/concave functions and for M-convex/concave functions as generalizations of Frank's discrete separation theorem for submodular/supermodular set functions and Edmon...

This paper shows the equivalence between Murota’s L-convex functions and Favati and Tardella’s submodular integrally convex functions: For a submodular integrally convex function g(p1, . . . , pn), the function g̃ defined by g̃(p0, p1, . . . , pn) = g(p1 − p0, . . . , pn − p0) is an L-convex function, and vice versa. This fact implies, in combination with known results for L-convex functions, tha...

We show that, up to automorphisms of P2 C, there are fourteen homogeneous convex foliations degree 5 on C. establish some properties the Fermat foliation Fd 0 d ≥ 2 and Hilbert modular F5H 5. As a consequence, we obtain that every reduced C is linearly conjugated one two F5 or H, which partial answer question posed in 2013 by D. Mar´in J. V. Pereira. end with conjectures about Camacho–Sad indic...